{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import trimesh\n",
    "import numpy as np\n",
    "from shapely.geometry import LineString\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# load the mesh from filename\n",
    "# file objects are also supported\n",
    "mesh = trimesh.load_mesh('../models/featuretype.STL')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# we're going to slice the mesh into evenly spaced chunks along z\n",
    "# this takes the (2,3) bounding box and slices it into [minz, maxz]\n",
    "z_extents = mesh.bounds[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# slice every .125 model units (eg, inches)\n",
    "z_levels  = np.arange(*z_extents, step=.125)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create an array to hold the section objects\n",
    "sections  = [None] * len(z_levels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i, z in enumerate(z_levels):\n",
    "    # this will return a Path3D object, each of which will \n",
    "    # have curves in 3D space\n",
    "    sections[i] = mesh.section(plane_origin = [0,0,z],\n",
    "                               plane_normal = [0,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# summing the array of path objects will put all of the curves\n",
    "# into one Path3D object, which we can then plot easily in 3D\n",
    "combined = np.sum(sections)\n",
    "combined.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD7CAYAAABpJS8eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x265f09b7588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we can also transform each section in space onto the XY plane\n",
    "# note that if the Path3D object couldn't find a plane which all \n",
    "# of the entities lie on, it will raise an exception\n",
    "section_2D, to_3D = sections[0].to_planar()\n",
    "section_2D.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<shapely.geometry.polygon.Polygon at 0x265f662ae80>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the polygons_full attribute contains every polygon and includes interiors\n",
    "section_2D.polygons_full"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "shapely.geometry.multilinestring.MultiLineString"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# if we want to intersect a line with this 2D polygon, we can use shapely methods\n",
    "polygon = section_2D.polygons_full[0]\n",
    "hits = polygon.intersection(LineString([[-4,0], [3,0]]))\n",
    "hits.__class__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD7CAYAAABpJS8eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x265edbbe780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we can plot the intersection (red) and our original geometry(black and green)\n",
    "for h in hits:\n",
    "    plt.plot(*h.xy, color='r')\n",
    "section_2D.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# if we want every section transformed using the same matrix \n",
    "# we can explicitly pass it to to_planar\n",
    "to_2D = np.linalg.inv(to_3D)\n",
    "all_2D = [i.to_planar(to_2D = to_2D) for i in sections]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD7CAYAAABpJS8eAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x265f85af7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the medial axis is available for closed Path2D objects\n",
    "(section_2D + section_2D.medial_axis()).show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
